A206712 Total number of distinct Hadamard matrices of order n.

2, 8, 0, 768, 0, 0, 0, 4954521600, 0, 0, 0, 20251509535014912000, 0, 0, 0, 88526812916367202104587059200000, 0, 0, 0, 3776127947893930552689423154306445475840000000, 0, 0, 0, 92624181047745713568610317051197596401168530978226831360000000, 0, 0, 0, 886156947284057553944669848348035536068124589065755283423684984832000000000000, 0, 0, 0

Offset: 1

Author

Brendan McKay, Feb 11 2012 (entered by N. J. A. Sloane)

Keywords

• nonn
• nice

Comments

a(n) is the total number of distinct Hadamard matrices of order n, ignoring all equivalences.

Links

• Brendan McKay, Table of n, a(n) for n = 1..35
• F. J. Aragon Artacho, J. M. Borwein, M. K. Tam, Douglas-Rachford Feasibility Methods for Matrix Completion Problems, March 2014.
• H. Kharaghani and B. Tayfeh-Rezaie, Hadamard matrices of order 32
• Index entries for sequences related to Hadamard matrices

Crossrefs

Cf. A007299, A036297, A206711.

Formula

a(4n) = A206711(n) = A048615(n)/A048616(n) * (2^n * n!)^2.

For n>1, a(4n+1) = a(4n+2) = a(4n+3) = 0.